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# What is the remainder when 4 ^96 is divided by 6 ? [CAT, 2003]

- May 30, 2018
- Posted by: allexamshelps
- Category: CAT

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3,697 total views, 1 views today

**Solution:**

**What is the remainder when 4 ^96 is divided by 6**

__Remainder__:

__Remainder__:

**Let’s have another similar example to solve such type of problem to understand the mathematics of remainder. Firstly, understand Euclid's division algorithm. The algorithm says any positive integer ‘a’ divided by a positive integer ‘b’ always leaves a remainder ‘r’ that is smaller than its divisor b.**

**a= bq+r, o≤ r<b, where**

**Practically, this means If I say, I want to divide a number by 6 then the remainder will always be less than 6, i.e., 0, 1, 2, 3, 4, 5. **

**Sample solution: Notice, when the exponent is even, the remainder, is 1. But when the exponent is odd, the remainder is 2. This happens in some cases.**

**2**^{2 }= 4 and \frac { 4 }{ 3 } = 1

^{2 }= 4 and \frac { 4 }{ 3 } = 1

**2**^{3} = 8 and \frac { 8 }{ 3 } = 2

^{3}= 8 and \frac { 8 }{ 3 } = 2

**2**^{4} =16 and \frac { 16 }{ 3 } = 1

^{4}=16 and \frac { 16 }{ 3 } = 1

**{ 2 }^{ 5 } =32 and \frac { 32 }{ 3 } = 2 **

** 2**^{6 }=64 and \frac { 64}{ 3 } = 1

^{6 }=64 and \frac { 64}{ 3 } = 1

**Now, the given problem, CAT 2003**

**4**^{2} = 16 and \frac { 16 }{ 6 } = 4

^{2}= 16 and \frac { 16 }{ 6 } = 4

**4**^{3} = 64 and \frac { 64 }{ 6 } = 4

^{3}= 64 and \frac { 64 }{ 6 } = 4

**4**^{5} = 1024 and \frac { 1024 }{ 6 } = 4

^{5}= 1024 and \frac { 1024 }{ 6 } = 4

**The remainder does not change for odd and even exponents. This means, no matter, what is the power of 4, the remainder is always 4. **

**Hence, the answer is 4 and the option (d) is correct.**

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